can someone show me examples of what is a practical application of matrices or matrix operations that can be used in a real-world situation.
Simple example: Coordinate transformation. An object is located at coordinates (x,y,z) in your coordinate system, what are the coordinates in some other coordinate system?
what do you mean in a coordinate location x,y,z?
In mathematics and physics, a coordinate system is a system that uses numbers, called coordinates, to uniquely determine the position of a point or an object. Each coordinate represents a direction or dimension in which the object can move or be located.
In the example I mentioned, the coordinates (x, y, z) represent a specific location or position in a three-dimensional space. The coordinate (x) corresponds to the horizontal direction, the coordinate (y) corresponds to the vertical direction, and the coordinate (z) corresponds to the depth or distance from the origin.
For instance, imagine you have a point in a 3D space representing the location of a house. The (x, y, z) coordinates could represent the longitude, latitude, and altitude of the house's location. So, if you know the coordinates (x, y, z) of the house in one coordinate system, you can use matrix operations to transform those coordinates into another coordinate system.
Matrix operations, like matrix multiplication and matrix addition, can be used to perform coordinate transformations. By multiplying a given coordinate vector by an appropriate transformation matrix, you can obtain the new coordinates in a different coordinate system.
This practical application of matrices and matrix operations is relevant in various fields, including computer graphics, robotics, navigation systems, and even in applications such as GPS technology, where converting coordinates between different systems is necessary for accurate positioning.